Problem: Assume this first statement is true: If it is Thanksgiving, then I will have a big dinner. Logically, can you deduce that this second statement must be true from the first one? If it is not Thanksgiving, then I will not have a big dinner.
Answer: Is the second statement the converse, inverse, or contrapositive of the original statement? The second statement is the inverse of the original statement. The inverse is not logically equivalent to the original statement, so no, the second statement cannot be deduced from the first statement.